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Degree reduction of Bezier curves and its error analysis

Published online by Cambridge University Press:  17 February 2009

Yunbeom Park  and
U Jin Choi
U Jin Choi
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Gu-sung Dong, Yu-sung Gu, Taejon, 305–701, Republic of, Korea.
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Abstract

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The error analysis of an algorithm for generating an approximation of degree n − 1 to an nth degree Bézier curve is presented. The algorithm is based on observations of the geometric properties of Bézier curves which allow the development of detailed error analysis. By combining subdivision with a degree reduction algorithm, a piecewise approximation can be generated, which is within some preset error tolerance of the original curve. The number of subdivisions required can be determined a priori and a piecewise approximation of degree m can be generated by iterating the scheme.

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 4 , April 1995 , pp. 399 - 413
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Boehm, W., Farin, G. and Kahmann, J., “A survey of curve and surface methods in cagd”, Comput. Aided Geometric Des. 1 (1984) 1–60.CrossRefGoogle Scholar
[2]Dannenberg, L. and Nowacki, H., “Approximate conversion of surface representations with polynomial bases”, Comput. Aided Geometric Des. 2 (1985) 123–131.CrossRefGoogle Scholar
[3]Farin, G., “Algorithms for rational Bézier curves”, Comput. Aided Des. 15 (1983) 73–77.CrossRefGoogle Scholar
[4]Farin, G., Curves and surfaces for computer aided geometric design (Academic Press, New York, 1988).Google Scholar
[5]Hersch, R. G., “Font rasterization: the state of the art”, 1991.Google Scholar
[6]Hoscheck, J., “Approximate conversion of spline curves”, Comput. Aided Geometric Des. 4 (1987) 59–66.CrossRefGoogle Scholar
[7]Petersen, C. S., “Adaptive contouring of three-dimensional surfaces”, Comput. Aided Geometric Des. 1 (1984) 61–72.CrossRefGoogle Scholar
[8]Sederberg, T. W. and Kakimoto, M., “Approximating rational curves using polynomial curves”, in NURBS for Curve and Surface Design (ed. Farin, G.), (SIAM, Philadelphia, 1991) 149–158.Google Scholar
[9]Watkins, M. A. and Worsey, J. A., “Degree reduction of Bézier curves”, Comput. Aided Des. 20 (1988) 398–405.CrossRefGoogle Scholar